The Rangers next play on Friday at Washington. Who will start in goal then for New York remains to be seen.
"It is safe to say that we're leaving for the holidays on a much happier note," Vigneault said. "It's going to be a pleasant three days.
"My parents are 81 and 79. I haven't been home for Christmas with my girls for eight years, so I am looking forward to that."
Miller, recalled from Hartford (AHL) on Thursday, scored his second of the season when he came off the bench, streaked down the slot, and took a crisp pass from Chris Kreider from behind the net.
Toronto nearly grabbed the lead just over four minutes into the third when Nikolai Kulemin was stopped in front and then had another drive hit the right post, slide along the goal line, and stay out. The no-goal call was confirmed by video review.
Bernier kept the Maple Leafs in it, especially during the second period when the Rangers had a 22-5 edge in shots. New York was dominant again in the middle frame one night after a 17-5 advantage against Minnesota when the Rangers scored twice.
"I don't think we played our best game, but we hung in there," Bernier said. "We stole a point probably."
Bernier got the starting nod from coach Randy Carlyle two nights after he replaced James Reimer, who was pulled against Detroit after giving up three goals on 12 shots in the first period. Bernier made 25 saves in relief, but Toronto was beaten in a shootout.
"Our goaltender stood on his head. That's all you can ask in a game like this one," Carlyle said.
NOTES: Talbot made back-to-back starts two other times this season but not on consecutive days. ... Rangers D Marc Staal took a hard skate Monday morning, while recovering from a concussion, and could be nearing a return. Staal missed his eighth game since he was struck in the head by the arm of New Jersey's Reid Boucher on Dec. 7. ... Reimer had started three straight games for the first time this season before Monday.